Problem: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 4)^2 - 49$
Explanation: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 4)^2 - 49 = 0$ Add $49$ to both sides so we can start isolating $x$ on the left: $ (x - 4)^2 = 49$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 4)^2} = \pm \sqrt{49}$ Be sure to consider both positive and negative $7$ , since squaring either one results in $49$ $ x - 4 = \pm 7$ Add $4$ to both sides to isolate $x$ on the left: $ x = 4 \pm 7$ Add and subtract $7$ to find the two possible solutions: $ x = 11 \text{or} x = -3$